Transmission network



April 24, 1934. w BQDE 1,955,788

TRANSMISSION NETWORK Filed Nov. 28, 1931 FIG. 7

A T TENUA TION A T'TENUA TION IN VENTOR H. W. 8005 A TTORNEY PatentedApr. 24, 1934 UNITED STATES PATENT OFFICE 1,955,788 TRANSMISSION NETWORKHendrik W. Bode, New

Bell Telephone Laboratories,

York, N. Y., assignor to Incorporated,

10 Claims.

This invention relates to electrical transmission networks of the typesknown as wave filters, phase correctors and delay networks and moreparticularly to a method of and means for regulating the attenuation ofsuch networks in the transmitted frequency band.

The principal object of the invention is to control the frequencyvariation of the attenuation in the transmission range of a network.Another object is to provide uniform attenuation in the band. A furtherobject is to eifect the compensation of attenuation distortion due toassociated apparatus or lines by means within the network.

It is well known that in wave filters, phase correctors and delaynetworks the attenuation over the band of frequencies transmitted is notzero. This attenuation is due in part to energy dissipation in thecomponent inductances and capacitances and, as a rule, is not uniformover the pass-band. In my prior Patent No. 1,828,-

454, dated October 20, 1931, it is shown that wave filters and delaynetworks having any desired characteristic may be constructed in theform of a symmetrical lattice or bridge the branches of which areconstituted by multiple resonant reactances of any degree of complexity.The most convenient forms of the branches comprise either a parallelconnected system of simple resonant combinations or a series connectedchain of antiresonant loops. In accordance with this invention thenetworks are preferably of the type described in my aforementionedPatent 1,828,454. The transmission characteristic of the network in itsrange of free transmission is controlled by the addition of properlychosen ohmic resistances in series with the resonant combinations or inparallel with the anti-resonant loops. The energy dissipation in theseadded resistances increases the attenuation of the network, with 0maximum effect at the resonant or anti-resonant frequency of the branchto which the resistance has been added. By properly proportioning theresistance values the points of low attenuation may be built up and thecharacteristic thereby made substantially flat, or it may be given someother desired shape. In certain cases these resistances can beincorporated in the inductances themselves so that no additionalelements are' required in order to provide the desired control.

In the following detailed description the application of the inventionto a broad band filter is described. It is to be understood, however,that the invention is not limited in its application to this type oftransmission network, but only in accordance with the appended claims.

Referring to the drawing:

Fig. 1 represents the general schematic form of the networks of theinvention;

Figs. 2, 3, 4 and 5 show typical forms of the network branch impedances;

Fig. 6 gives symbolically the reactance characteristics of the branchimpedances of Figs. 2, 3, 4 and 5; and

Figs. '7 and 8 shows typical transmission characteristics obtained bythe invention.

The network of Fig. 1 is of the lattice or bridge type, comprising twoequal line impedances Z1 and two equal impedances Z2 connecteddiagonally between the input and output terminals. It is shown connectedbetween terminal impedances Z5 and Za which may represent, for example,portions of a telephone system or other apparatus, a wave source ofelectromotive force E being included in series with one of the terminalimpedances Zs. The impedances Z1 and Z2 are primarily reactances and mayhave any degree of complexity and any of a wide variety of schematicforms. Preferred forms of the branch impedances are those illustrated inFigs. 2 to 5 inclusive, the type illustrated in Figs. 2 and 3 comprisinga plurality of resonant circuits connected in parallel and the typeshown in Figs. 4 and 5 comprising a plurality of anti-resonant circuitsconnected in series. In the former type a small resistance is includedin each resonant circuit and the whole impedance may be shunted by ahigh resistance. In the latter type each anti-resonant circuit isshunted by a high resistance and a small resistance may be included inseries with the whole impedance.

The principles of the invention will be explained in connection withtheir application to a low-pass filter having branch impedances Z1 andZ2 corresponding to Figs. 2 and 3 respectively. In this case theimpedance Z1 comprises a parallel connected system of five resonantcircuits, shunted by a resistance Ba and having an ohmic resistance inseries with each resonant circuit.

In the figure each resonant branch is designated by its frequency ofresonance, f0, f2, f4, etc. The variation of the reactance o-f Z1 isshown symbolically by the solid-line curve of Fig. 6 in which abscissaerepresent frequency, and the ordinates the values of the reactance. Thereactance is zero at Zero frequency, is alternately infinite and zero atthe successive frequencies f1, f2, f3, f8, and is infinite at infinitefrequency.

If it is desired that the network shall have a single pass-bandextending from zero to is, the necessary variation of Zz follows readilyfrom the requirement that Z1 and Z2 shall have opposite signs everywherethroughout the band and shall have the same sign everywhere outside theband. The dotted curve of Fig. 6 shows the reactance characteristicrequired for Z2, having infinite values at zero frequency, f2, f4, f7and infinity, and zero values at f1, f3, fs and is. Fig. 3 shows asuitable structure for Z2, composed of four resonant circuits connectedin parallel, a shunting resistance Rb and an ohmic resistance in serieswith each resonant circuit being added for attenuation control purposes.Each resonant branch is designed by its frequency of resonance.

The resistances shown in series with the resonant branches of Figs. 2and 3 cause a certain amount of energy dissipation which serves toincrease the attenuation of the filter in the passband. The increase inattenuation due to any particular resistance is greatest at theresonance frequency of the circuit in which the resistance is located,because at that frequency the current through that branch is a maximumand the energy dissipation in the resistance is also a maximum. Theresistance Ra shunting impedance Z1 has its maximum effect in increasingthe attenuation of the network at the anti-resonant frequencies of Z1,and, similarly, Rb has its maximum effect at the anti-resonantfrequencies of Z2. It will be seen, therefore, that in the passband.there are five frequencies, namely, zero, f1, f2, f3 and T4, at whichcontrol of the attenuation of the network is provided. By proper choiceof the individual resistances the attenuation characteristics of thenetwork may be given any desired shape, within wide limits. For example,the attenuation of the filter of Fig. l, which, without addedresistances, is shown symbolically by the dotted curve of Fig. 7, can,by the addition of theproper resistances, be leveled out in thepass-band as shown by the solid-line curve of Fig. '7. Where theattenuation is low it is built up by the addition of resistances whichhave their greatest effect over that frequency range. As a concreteillustration it will be assumed that the filter is to have a constantattenuation within the transmission band equal in magnitude to fourdecibels, the attenuation of the unequalized filter at some particularfrequency near its cut-off. It will be further assumed that theattenuation of the unequalized filter at the frequency I1 is onedecibel, which value has been determined by measurement or by well knownmethods of computation, taking into account the dissipation in 7 thereactive elements. It is necessary, therefore,

to increase the attenuation of the filter at 1 from one decibel to fourdecibels. In accordance with the invention this is accomplished byincreasing by a factor of four the resistance effectively in series withthe resonant f1 arm of the Z2 impedance branch, shown in Fig. 3. If theuncorrected resistance component of the f1 arm at resonance is two ohms,as measured on an impedance bridge or as calculated, then thisresistance must be increased to eight ohms, by the J addition of a sixohm resistance in series with the f1 arm. Similarly, if the attenuationat the frequency 2 is to be increased from say two decibels to therequired four decibels, then it is necessary'to increase the effectiveresistance of the resonant f2 arm of the Z1 impedance branch, shown inFig. 2, to twice its former value. If the effective resistance of thisarm before corrcction is three ohms at the resonant frequency, then athree ohm resistance must be added in series with the harm. In the sameway, the attenuation of the filter is built up to four decibels at theother critical frequencies within the passband, namely, zero, is and f4,by the addition of an ohmic resistance in series with the arm of theimpedance branch which is resonant at the par ticular frequency.

In a similar manner the attenuation of the filter in its transmissionrange may be given a downward slope with increasing frequency, as shownby the solid-line curve of Fig. 8. Such an attenuation characteristicwould be useful, for

example, in compensating the attenuation distor' tion of an associatedtransmission line or other apparatus having attenuation which increaseswith frequency in a complementary manner as indicated by the dotted-linecurve of Fig. 8.

In certain cases the resistances Ra and Rh may Fig. 4 shows analternative form for Z1 consisting of a chain of anti-resonant loopswith a resistance shunting each loop and a resistance R0 in series withthe chain. In the figure each antiresonant loop is designated by itsfrequency of anti-resonance, f1, 3 etc. Each shunting resistance has itsmaximum effect in increasing the attenuation of the filter at theanti-resonant frequency of the loop which the resistance shunts. Theseries resistance Re is most effective in increasing the filterattenuation at the resonant frequencies of Z1. In certain cases thisresistance may be omitted and, if desired, each of the shuntingresistances may be replaced by a small resistance in series with theinductance of the antiresonant loop so chosen as to give at theantiresonance frequency of the loop the same effective resistance as theshunting resistance. This resistance in series with the inductance canthen be incorporated into the effective resistance of the inductance. Inthis way no additional resistance elements are required in order toprovide effective attenuatiton control for the filter. An alternativeform for Z2 comprsing a chain of antiresonant loops is shown in Fig. 5.The above discussion of the resistances of Fig. 4 applies with equalforce to the resistances of Fig. 5.

In order to avoid a duplication of the impedances Z1 and Z2 the networksof the invention may, of course, be converted from the lattice formshown in Fig. l to a bridged-T form, as described L in my aforementionedPatent 1,828,454. The latter form comprises a bridging branch having theimpedance prising a plurality of branches, the impedances of two of saidbranches being adapted to determine the transmission characteristics ofsaid network, said impedances each having a plurality of criticalfrequencies defining resonances and antiresonances and beingproportioned to provide a free transmission band, and a resistanceincluded in one of said branches, said resistance being so disposed insaid branch that its value determines the magnitude of the impedance ofsaid branch at one of said critical frequencies, and the value of saidresistance being so chosen that said network has a predeterminedattenuation at said one critical frequency.

2. A wave transmission network comprising a plurality of branchimpedances, two of said impedances being adapted to determine thetransmission characteristics of said network, said two impedances eachhaving a plurality of critical frequencies and being proportioned toprovide a free transmission band, and a resistance included in at leastone of said impedances for controlling the effective resistance of saidimpedance at one of said critical frequencies, whereby said network isgiven a predetermined attenuation at said one critical frequency.

3. A four-terminal transmission network comprising a plurality of branchimpedances, two of said impedances being adapted to determine thetransmission characteristics of said network, said two impedances eachhaving a plurality of critical frequencies and being proportioned toprovide a free transmission band, and the effective resistance of saidimpedances being given predetermined values at said critical frequencieswhereby the attenuation characteristic of the network is made to followa desired curve throughout the transmission band of said network.

4. A wave transmission network comprising a plurality of multipleresonant branch impedances having a plurality of critical frequencies ofresonance and anti-resonance, two of said impedances being adapted todetermine the transmission characteristics of said network, theattenuation of said network being determined at a certain frequencywithin said transmission band by providing a predetermined effectiveresistance for at least one of said branch impedances at a criticalfrequency near said certain frequency, whereby the attenuation of saidnetwork is made to coincide at said certain frequency, with anarbitrarily chosen attenuation curve.

5. A wave transmission network comprising two pairs of equal impedancesarranged to form a symmetrical lattice structure, said impedancescomprising multiple resonant reactances, the resonances of the one paircoinciding with the anti-resonances of the other pair in a preassignedbroad frequency range to provide free transmission, and the effectiveresistance of said impedances being controlled at the resonant andanti-resonant frequencies by energy-dissipating means within saidimpedances whereby the attenuation of said network in the transmittingrange is made substantially uniform.

6. A four-terminal transmission network comprising two pairs of equalimpedances arranged to form a symmetrical lattice structure, each ofsaid impedances having a plurality of critical frequencies, theresonances of the one pair coinciding with the anti-resonances of theother pair in a preassigned broad frequency range to provide freetransmission, and energy dissipating means within at least one of saidimpedances for controlling the eifective resistance of said impedance atone of said critical frequencies, whereby the attenuation of saidnetwork is made substantially uniform throughout its transmission range.

7. A wave transmission network comprising two pairs of equal impedancesarranged to form a symmetrical lattice structure, at least one pair ofsaid impedances each comprising a resistance in parallel with aplurality of resonant branches, each of said branches comprising aninductance, a capacitance and a resistance in series relation. theattenuation of said network being determined at the critical frequenciesof said impedances by the individual values of said resistances and saidvalues being so chosen that the curve of said attenuation conforms to adesired shape in the transmission range of said network.

8. A four-terminal transmission network comprising two pairs of equalimpedances arranged to form a symmetrical lattice structure, at leastone pair of said impedances each comprising a resistance in series witha chain of anti-resonant loops, with a separate resistance shunting eachof said loops, the attenuation of said network being determined at thecritical frequencies of said impedances by the individual values of saidresistances and said values being so chosen that the curve of saidattenuation conforms to a desired shape in the transmission range ofsaid network.

9. In combination a network in accordance with claim 3 and associatedapparatus, said associated apparatus having an attenuationcharacteristic which is not uniform in the transmission band of saidnetwork, and the effective resistance of the branch impedances of saidnetwork being so chosen that the attenuation char acteristic of thenetwork substantially compensates the attenuation distortion of saidassociated apparatus.

10. A wave transmission network comprising a plurality of branchimpedances, two of said impedances being adapted to determine thetransmission characteristics of said network, said two

